Maximum cardinality search on undirected graph.

Returns (if it exists) a perfect ordering of the vertices in an undirected graph.

mcs(object, root = NULL, index = FALSE)

# Default S3 method
mcs(object, root = NULL, index = FALSE)

mcsMAT(amat, vn = colnames(amat), root = NULL, index = FALSE)

mcs_marked(object, discrete = NULL, index = FALSE)

# Default S3 method
mcs_marked(object, discrete = NULL, index = FALSE)

mcs_markedMAT(amat, vn = colnames(amat), discrete = NULL, index = FALSE)

Arguments

object

An undirected graph represented either as a graphNEL object, an igraph, a (dense) matrix, a (sparse) dgCMatrix.

root

A vector of variables. The first variable in the perfect ordering will be the first variable on 'root'. The ordering of the variables given in 'root' will be followed as far as possible.

index

If TRUE, then a permutation is returned

amat

Adjacency matrix

vn

Nodes in the graph given by adjacency matrix

discrete

A vector indicating which of the nodes are discrete. See 'details' for more information.

Value

A vector with a linear ordering (obtained by maximum cardinality search) of the variables or character(0) if such an ordering can not be created.

Details

An undirected graph is decomposable iff there exists a perfect ordering of the vertices. The maximum cardinality search algorithm returns a perfect ordering of the vertices if it exists and hence this algorithm provides a check for decomposability. The mcs() functions finds such an ordering if it exists.

The notion of strong decomposability is used in connection with
e.g. mixed interaction models where some vertices represent
discrete variables and some represent continuous
variables. Such graphs are said to be marked. The
\code{mcsmarked()} function will return a perfect ordering iff
the graph is strongly decomposable. As graphs do not know about
whether vertices represent discrete or continuous variables,
this information is supplied in the \code{discrete} argument.

Note

The workhorse is the mcsMAT function.

See also

moralize, junction_tree, rip, ug, dag

Author

Søren Højsgaard, sorenh@math.aau.dk

Examples

uG <- ug(~ me:ve + me:al + ve:al + al:an + al:st + an:st)
mcs(uG)
#> [1] "me" "ve" "al" "an" "st"
mcsMAT(as(uG, "matrix"))
#> [1] "me" "ve" "al" "an" "st"
## Same as
uG <- ug(~ me:ve + me:al + ve:al + al:an + al:st + an:st, result="matrix")
mcsMAT(uG)
#> [1] "me" "ve" "al" "an" "st"

## Marked graphs
uG1 <- ug(~ a:b + b:c + c:d)
uG2 <- ug(~ a:b + a:d + c:d)
## Not strongly decomposable:
mcs_marked(uG1, discrete=c("a","d"))
#> 'as(<ddiMatrix>, "dgCMatrix")' is deprecated.
#> Use 'as(as(., "generalMatrix"), "CsparseMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
#> character(0)
## Strongly decomposable:
mcs_marked(uG2, discrete=c("a","d"))
#> [1] "a" "d" "b" "c"